In the symmetric case \((\ell _1=\ell _2=\ell )\) , in [1]}, for \(f\in {L} \)  with bounded type rotation number, the author shows that, if \(\ell \in (1,2]\) , then the Hausdorff dimension of the
non-wandering set is equal to zero and that,
if \(\ell >2\) , then the Hausdorff dimension of the non-wandering set is strictly greater than zero. This result generalizes the one in [2]} where the author treats the maps in \({L} \)  with critical exponents \((1,1)\) . Let us note that, the results in [1]} are more general (they only depend on geometry) ; precisely, if the rotation number is the bounded type, then, the Hausdorff Dimension of the non-wandering set is equal to zero when the geometry is degenerate and it is strictly greater than zero when the geometry is bounded ; so we have the following result which is proved at the end of the paper.
